Chap 5

Choose the statement that best defines the term "experiment" in the context of probability.

A process that leads to only one of several possible outcomes.

Consider the experiment of rolling a die. The event getting a 2 and which ONE of the following would be considered mutually exclusive?

Getting a 4.

In a probability experiment involving rolling a die, which of the following is an outcome? Select all that apply.

Getting a 6 Getting a 2

Given an experiment of rolling a die and the event getting an even, which of the following event that make the set of events collectively exhaustive events?

Getting an odd

Given an experiment of rolling a die and the event getting an even, which of the following event that make the set of events collectively exhaustive event?

Getting an odd.

Which of the following are true regarding the special rule of addition and the general rule of addition? Select all that apply.

If the events A and B are mutually exclusive, you can use the special rule of addition. If the events A and B are not mutually exclusive, you can use the general rule of addition.

In the Venn diagram shown, what is the joint probability?

P(A and B)

Which of the following formulas correctly represents the general rule of multiplication for two events?

P(A and B) = P(A)P(B|A)

"The probability that even A will occur is forty-five percent." Which of these statements correctly expresses this statement in mathematical form?

P(A) = 0.45

In the Venn diagram shown, what does the area inside the circle labeled "Event B" represent?

P(B)

If events A and B are mutually exclusive and collectively exhaustive, which one of the following is true?

Probability of A= 1 - Probability of B

What does it mean when an experiment has a set of events that are collectively exhausted?

That at least one of events must occur.

What is the assumption upon which classical probability is based?

That the outcomes of an experiment are equally likely.

As the number of trials increases, what does the law of large numbers say about the probabilities?

The empirical probability will approach the event's true probability.

Which of the following is a subjective probability?

You apply for a particular job after graduation and you estimate your chance of getting the job at 83%. (You can't apply for the job many times and see how many times you get it.)

Two events are independent if:

the occurrence of one event does not change the likelihood that the other will occur. Probability Notation: P(A|B)= P(A)

Two events are mutually exclusive if:

the occurrence of one event means the other can't occur at the same time One "excludes" the other.

Choose the formula that correctly describes the special rule of multiplication.

P(A and B)= P(A)P(B)

Which one of the following condition must be met to use the special rule of addition? I.e. P(A or B)=P(A) + P(B)

The events A and B must be mutually exclusive.

Which of the following best describes the meaning of "outcome" in the context of a probability experiment?

A particular result of the experiment.

Which of the following numbers could represent a probability that an event will occur? Select all that apply.

.43 3/4 25%

Study the Venn diagram shown. What is the value of P(E or F)?

.60 P(E or F) = .40 + .30 - .10

Suppose that P(X)= 0.20, P(Y)= 0.40, P(Z)= 0.25, and the events are mutually exclusive. What is the probability of X, Y, or Z occurring?

.85

If P(J)=0.4 and P(Z)=0.3, what is the probability that J and Z occur together? Assume the events are independent.

0.12

Suppose that P(A)= 0.20, P(B)= 0.30, and the events are mutually exclusive. What is the probability of A or B occurring?

0.5

If P(Z)= 0.25, the P( ~Z) is

0.75

Using the contingency table shown here, calculate the empirical probability that a randomly chosen person was a man and attended 2 or more movies last month.

1/15

The probability of rolling a one with a die is 1/6. What is the probability of rolling two ones with two dice?

1/36 P(A and B)= P(A)P(B)

Using the contingency table shown here, calculate the empirical probability that a randomly chosen person was a woman and attended 1 movie last month.

1/5 30/150=1/5

Using the contingency table shown here, calculate the conditional probability that a randomly chosen man saw two or more movies last month.

1/7 P(2+|M)=10/70

Using the contingency table shown here, calculate the conditional probability that had a randomly chosen man saw two or more movies last month.

1/7 P(2+|M)=10/70

In a random experiment there are 8 possible outcomes, and two of them correspond to a favorable event. What is the classical probability of the event?

25%

Using the contingency table shown here, calculate the empirical probability that someone who attended only one movie last month is a woman.

3/7 P(F|1)=30/70

A first place, second place, and a third place winners will be selected from 8 people who entered a contest. How many ways can the prized be given out?

336 8 P 3= 8!/(8-3)!= 8*7*6

Given the following contingency table, how many conditional probabilities are listed for the second set of branches? Assume 'Movies Attended' is represented as the first stage of the tree diagram.

6 for each category of 'movies attended,' there are two branches (one for each gender)

what does 5!/2! equal?

60

When you flip three coins, the probability that they will show three "heads" is 1/8. What is the probability they will NOT show 3 heads?

7/8 Let 3 heads=A. Then P(~A)=1-P(A)=1-1/8

Mary has tickets to a concert. She wants to give four of them to her friends. If she has eight friends and only gives one ticket to each person, how many different ways can she distribute them?

70 (nCr) (8C4)= 8!/4!(8-4)!

Which of the following is the best definition of "event" in the context of a probability experiment?

A set of one or more outcomes of an experiment.

Identical prizes are to be given to two winners from a group of 12 contestants. What counting formula would you use to determine how many ways the prizes could be given out?

Combination formula

The equation P(A)=1-P(~A) is known as the rule.

Complement

What is the name of a table, such as the one shown, that shows the relationship between two variables?

Contingency Table

If the fraction of times an event happened in the past is used as the basis for assigning a probability to the event , this is Probability.

Empirical

Suppose a college student is asked his major. Match the term to the part of the random trial to which it refers.

Experiment- The process of asking his major . (The experiment leads to the occurrence of the outcomes and events.) Outcome- The student is an insurance major. (An outcome is a particular result of the experiment.) Event- The student is a business major. (More than one outcome can lead to this event.... accounting finance marketing .....)

The value given for an empirical probability is based on:

The past history of outcomes from the experiment i.e. the frequency distribution.

How would you read the formula P(~A)?

The probability of not A.

For two independent events, which statement correctly describes the special rule of multiplication?

The probability that both events will occur is found by multiplying the individual probabilities. I.e. P(A and B)= P(A)P(B)

A bowl contains three red and four yellow marbles. You randomly select two marbles from the bowl. Which of the following is a conditional probability? Assume the second marble is drawn from the marbles remaining after the first draw.

The probability that the second marble will be red, if the first one was yellow.

Choose the best description of a joint probability.

The probability that two or more events will happen at the same time.

A permutation is any arrangement of r objects selected form n possible objects. Which formula is used to calculate the number of permutations?

nPr= n!/(n-r)!

A permutation is any arrangement of r objects selected from n possible objects. Which of the following is not true?

r can be greater than n

Consider the experiment of rolling a die. The event getting a 2 and which one of the following would be considered mutually exclusive?

Getting a 4

The chance of drawing a spade from a deck of cards is 1/4. If the deck is shuffled between draws, what is the probability of drawing two spades in two draws if the first card is returned to the deck between draws.

1/16 (1/4)(1/4)=(1/16)

Using the contingency table shown here, calculate the empirical probability that a randomly chosen person was a woman or attended 1 movie last month.

4/5 (80+70-30)/150=120/150=4/5

Quickie Pizza sell just 10-inch cheese and pepperoni pizzas. The pepperoni pizza comes in three types of crust, three types of sauce, and two types of pepperoni. How many different types of pepperoni pizzas doe Quickie Pizza make?

18